HW3-Solutions.pdf - nrqu-qh n;m-t.~.m-myu.~s 6.10 64...

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Unformatted text preview: n—rqu-qh. — n;m-t.~..—m-myu-.~s. .. 6.10 64! Bl‘osrarzotzm Hw 500mm HWS 6.10 5.0 6.!) 6.15 6ng 6.17 Exercise 10 a. The probability that the principal source of payment is private insurance is 0.387. b. Since the sources of payment are all mutually exclusive, the probability that the principal source of payment is Medicare, Medicaid, or some other government program is P(Medicare or Medicaid or other) = P(Medicare) + P(Medicaid) + P(other) = 0.345 + 0.116 + 0.033 = 0.494. c. Given that the principal source of payment is a government program, the probability that it is Medicare is P(Medicare and government program) P(governrnent program) P(Medicare) P(gcwernment program) 0.345 0.494 0.698. ll P(Medicare I government program) Exercise 11 a. Since these events are independent, the probability that both adults are uninsured is P(both uninsured) = P(wornan uninsured) x P(man uninsured) 0.123 X 0.123 0.015. b. The probability that both adults are insured is P(both insured) = (1 — 0.123) x (1 — 0.123) = 0.877 x 0.377 = 0.709. c. The probability that all five adults are uninsured is 0.123 x 0.123 x 0.123 x 0.123 x 0.123 = 0.000028. 6"} Exercise 13 a. The probability of a. false negative result is P(—- test { ca.) = 1 — sensitivity 1 — 0.85 0.15. H b. The probability of a false positive result is P(+ test | no ca) = 1 — specificity = 1 — 0.80 = 0.20. i ! c. Since P(ca.) = 0.0025 and P(no ca) = 0.9975, the probability that a woman has breast cancer 1 - given that her mammogram is positive is P(ca)P(+ test I ca.) P(ca)P(+ test [ ca) + P(no ca)P(+ test | noca) (0.0025)(0.85) (0.0025)(0.85) + (o.9975)(o.20) 0.0105. P(ca l + test) = 6, '5 Exercise 15 a. The sensitivity of radionuclide ventriculography is 302 481 * 0.628, P(+rv \ cad) ll and its specificity is 313 452 = 0.823. P(—rv I no cad) b. Since P(cad) = 0.10 and P(no cad) = 0.90, the probability that an individual has coronary artery disease given that he or she tests positive is P(+rv [ cad)P(cad) P(+rv I cad)P(cad) + P(+rv i no cad)P(no cad) (0;628)(0.10) (0.628)(0.10) + (0.177)(0.90) = 0.283. P(cad I +rv) c. The predictive value of a negative test is ‘ P(—rv 1 no cad)P(no cad) P(—rv | no cad)P(no cad) + P(—rv l cad)P(cad) (0.823)(0.90) (0.823)(0.90) + (o.372)(o.10) 0.952. P(no cad | —rv) = usumxmmnmm vvmurvaemmumn maummmflmmmmmmwmmvwmflmfl s:unu,:-n~w>\n mm‘ua‘rvk‘l a 648 647 Exercise 18 The relative risk of pregnancy for women using a particular contraceptive method versus women not using any type of protection is calculated as RR P(pregnancy | method) P(pregnancy I no protection) P(pregnancy f method) 0.431 ' Note that each of the relative risks below takes a value less than 1, indicating that each of the methods carries a lower risk of pregnancy than no protection at all. The Pill has the smallst relative risk (least risk, relative to no protection), and the diaphragm the largest. Method of Contraception Relative Risk . Diaphragm 0.346 Condom 0.246 IUD 0. 165 Pill 0. 086 Exercise 19. a. The probabilities of sufl'ering from persistent respiratory symptoms by socioeconomic status are shown below. Socioeconomic Status Probability Low 0.392 Middle 0.238 High 0.141 b. Let 5’ represent the presence of symptoms. The odds of experiencing persistent respiratory symptoms for the middle group relative to the high group are P(S l middle) /[1 — P(S | middle)] P(S | high) /[1 — P(S’ I high)] (0.238) /(1 — 0.238) (0.141)/(1 — 0.141) = 1.90, OR: I! and for the low group relative to the high group are P(S | low)/[1— P(S | low)] P(5 | hish)/[1 - P(5 I high” (0.392) /(1 — 0.392) (0.141) /(1 — 0.141) = 3.93. OR c. There does appear to be an association between socioeconomic status and respiratory symptom; the odds of experiencing symptoms increase as socioeconomic status decreases. ...
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